Statistical Process Control ("SPC") methods generally are well-known statistical tools for helping manufacturers monitor and analyze measurements of response variables observed from their machines or processes to make sure that the machines or processes are operating properly and to identify when they are not operating properly. Machines and processes that are operating properly are said to be operating "in control" and machines and processes not operating properly are said to be operating "out of control." SPC methods are typically built around the idea that measurements of response variables taken from a process or machine can be described as approximately statistically "normal". When these "normal" data are plotted in the order in which they are observed originating from the process, the data form a kind of cloud that is most dense near the center or average with gradual thinning out as the values increasingly differ from the average. FIG. 1 shows a plot of a sample set of data points which is approximately "normal" with an average value or centerline 6.
The graph shown in FIG. 2, a "normal" curve, demonstrates the relationship between the observed data points shown in FIG. 1 and the frequency of their occurrence. FIG. 2 demonstrates that the data value with the highest frequency 8 corresponds to the average value 6 in FIG. 1.
As an example of normal data collected from a process or machine, consider a machine designed for cutting strips of plastic at a pre-set length of 6 inches from a continuous role of plastic. In this case, one response variable might be the length of each plastic strip. While the expected average length of each cut plastic strip is 6 inches, it is not unusual that each plastic strip will not be exactly 6 inches long. That is, the machine is still considered to be operating properly if, within a sample of a particular number of plastic strips produced by the machine, there is a variance in the lengths of the individual plastic strips, provided however, that as the variance between the actual length of the plastic strips and the expected length (6 inches) increases, the frequency of such occurrences decreases. In other words, if the lengths of all of the sample plastic strips were plotted as in FIG. 1, most of the values would hover slightly above or slightly below 6 inches with some values straying further away from 6 inches, but with less frequency. SPC methods depend upon measurements of response variables observed from a process or machine conforming to a "normal" probability distribution.
SPC analysis begins by calculating the average value of a response variable and the associated standard deviation while the machine or process is known to be operating in control. Then, when the machine or process is operating on an ongoing basis, observed measurements of the response variable are compared to the known average and standard deviation.
Various simple well-known SPC rules have been developed to assist operators to determine if their machines or processes are no longer operating properly, or have fallen "out of control." The rules are designed to look for patterns in the response variables observed from the machine or process. The decision criteria to determine if the machine or process is out of control are typically set so that a pattern would rarely happen by chance alone under the assumed condition that the data are "normal" and centered on some constant average value. For example, an operator applying one particular SPC rule would check to see if at least 4 out of 5 consecutive observed values of a particular response variable are on the same side of the calculated centerline, i.e., the response variable's calculated average value under normal operating conditions, and are outside of the upper or lower control limit (set at 1 standard deviation above and below the average for purposes of this SPC rule). Under ideal operating conditions, these two conditions in the rule would only be satisfied simultaneously about once in every 360 data values. Because the pattern almost never happens by chance alone, the operator can be reasonably confident that the occurrence of this pattern means that the assumed condition, that is that the machine or process is still in control and the actual mean value of the observed data is the same as the calculated average value, is no longer valid. For instance, in the previously-described example regarding the processing of plastic strips, if the operator of the machine were to observe the 4 out of 5 rule being violated, he could conclude that the machine for some reason was no longer operating in control, and that the actual mean length of the strips being produced was no longer 6 inches. Accordingly, the violation of the 4 out of 5 rule would suggest that investigation is needed and that actions may be needed to restore the machine or process to its steady state control condition. There are many well-known SPC rules, but most depend upon comparing observed response variable measurements to known calculated response variable averages and upper and lower control limits, which are generally derived from standard deviation calculations.
SPC rules, like the 4 out of 5 rule described above, are very simple to use. Indeed, busy operators can use simple SPC rules to make quick decisions about the need for action when they use SPC charts to monitor processes or when computers or central processors analyze the data automatically. The SPC rules are theoretically applicable to virtually any process or machine that has a response variable with a constant mean or average value that can be measured and monitored. But in semiconductor manufacturing, the simple SPC rules are not easily applicable and have not been used effectively in the industry for many processes because many of the variables of processes in the semiconductor manufacturing industry do not have a constant expected value. Instead, many of the measurements of such processes are expected to have a varying mean value as the machine or process is used. Traditional applications of SPC rules are not equipped to account for varying mean values, and are therefore ineffective as applied to such machines or processes.
For example, a semiconductor manufacturer may use atmospheric pressure chemical vapor deposition ("CVD") equipment to make a glass film. As the equipment runs, the exhaust deposits on equipment parts changing the pressure which in turn changes the thickness of the glass deposition on the wafer. With that CVD equipment, users expect the process and therefore the value of response variables to change over the period of use.
Another example is the use of an etcher that has a manually adjusted electrode. As the equipment is used, the electrode wears out. As the electrode wears out, the gap changes and the wafer is affected. Again, in such a process, the operator expects that the mean value of response variables observed from the wafer will change over the period of the process. Thus, traditional application of SPC rules which depend upon a constant mean value would be ineffective to monitor the process.
Finally, a third example of semiconductor manufacturing processes that have expected varying mean response variables is found in the sputtering process, wherein a layer of aluminum is deposited on the surface of a semiconductor wafer. The aluminum is deposited on the wafer by eroding it off of an aluminum source target. As machine hours of the sputtering equipment are accumulated, the aluminum thickness deposited in a fixed amount of sputtering time will change because there is less aluminum on the source target. Sequential wafers are expected to receive less aluminum unless the sputtering time is increased. Therefore, if sputtering time is set as a constant, the sputtering process is expected to have a pattern of continually-reduced aluminum thickness both on the source target and the wafers as more wafers are processed. Typically, to maintain a minimum level of aluminum being deposited on the wafers, the level of aluminum on the target source is readjusted periodically. As a result, the process centerline or mean thickness of aluminum deposited on the wafer is expected to vary as the aluminum on the target source diminishes and as it is replenished periodically. Accordingly, the mean value of the aluminum thickness on the wafer is not expected to be a constant, and traditional application of SPC rules to monitor and analyze the thickness level of aluminum in a sputtering process is not effective.
Accordingly, a method, and apparatus for implementing that method, for applying SPC rules to monitor and analyze semiconductor manufacturing processes is desirable.